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研究生:莊啟祥
研究生(外文):Chi-Hsiang Chuang
論文名稱:以分子動力學研究奈米碳管之振動行為
指導教授:張怡玲
指導教授(外文):I-Ling Chang
口試委員:劉德騏鄭志鈞張國恩
口試委員(外文):De-Shin LiuChin-Chun ChengGuo-En Chang
口試日期:2014-06-11
學位類別:碩士
校院名稱:國立中正大學
系所名稱:機械工程學系暨研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:107
中文關鍵詞:奈米碳管分子動力學初始模態快速傅立葉轉換振動分析
外文關鍵詞:CNTmolecular dynamicsinitial displacement of mode shapefast Fourier transformvibration analyze
相關次數:
  • 被引用被引用:0
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  • 下載下載:10
  • 收藏至我的研究室書目清單書目收藏:1
本研究以分子動力學結合振動分析方法,研究奈米碳管在受到拉壓應力下及施加初始模態位移大小對共振頻率的影響,藉由快速傅立葉轉換處理分子模擬中輸出之原子速度與時間序列以及位置與時間序列,系統性的針對奈米碳管主要振動模式(軸向及橫向)進行分析,並繪製出其模態圖作為對照。
由模擬結果發現碳管拉伸(壓縮)越大則軸向振動的頻率會下降(上升);橫向振動的第一振動頻率隨著碳管拉伸而持續升高,但是對橫向振動的較高頻率则無明顯影響。此外,施加初始模態位移大小並不會影響碳管之橫向共振頻率,但由頻譜圖可明顯觀察到該模態的頻率參予量升高,但如果所施加的初始模態位移太大,碳管容易在模擬過程中發生挫曲,一旦挫曲發生則不易從頻譜圖中辨識共振頻率。
另外也對銅奈米線的振動行為加以探討,銅奈米線為實心結構,原子數量較多,如果對所有原子的振動進行分析,則處理的數據量相當龐大,因此以不同取樣方式進行頻率分析,發現取樣方式對共振頻率的值並不會有太大的影響,只有在求對應的模態時,不同取樣方式才會有所差異。
The vibrational behavior of CNTs and copper nanowires were analyzed using molecular dynamics (MD) combined with conventional vibration analysis. The temporal information of displacements and velocities extracting from molecular dynamics simulation were converted into frequency domain using fast Fourier transform (FFT). The primary vibrations (i.e., lateral and longitudinal) and their corresponding mode shapes were analyzed. We investigated the influence of axial loading and initial modal displacement on the natural frequency of CNTs. Since copper nanowires are solid structures as compared to hollow CNTs, the number of atoms was higher and it would be challenging to analyze such huge amount of data. Hence, we studied the correctness of efficiency of various sampling methods in order to extract the resonance of nanowires.
From the analysis, it was observed that the longitudinal frequencies decreased and the first lateral resonance frequencies increased while pulling the CNTs. However, the axial loading did not have obvious effect on higher lateral resonance. Furthermore, the initial applied modal displacements would only increase the response of the corresponding frequencies in spectrum and their frequencies remained the same. However, if the magnitude of initial displacements were too large, it is possible that buckling would appear, under which condition the resonance would be difficult to identify. About the vibrational analysis of copper nanowire, it was noticed that the sampling methods would not affect the identification of resonant frequencies as long as the sampling atom percentage is not too low. However, the characterization of mode shapes would be significantly influenced by the sampling methods.
誌謝 I
摘要 II
ABSTRACT IV
目錄 V
圖目錄 VIII
表目錄 XII
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 本文架構 4
第二章 分子動力學 6
2.1 基本理論與假設 6
2.2 系綜觀念 7
2.3 分子作用力與勢能函數 8
2.3.1 作用力 8
2.3.2 勢能函數 9
2.4 原子級應力 15
2.5 週期性邊界條件與最小映像法則 16
2.5.1 週期性邊界條件 16
2.5.2 最小映像法則 17
2.6 初始條件設定 18
2.7 運動方程式 19
2.8 截斷半徑法與VERLET表列法 22
2.9 系統平衡 24
2.10 原子模型 25
第三章 碳管振動分析 37
3.1 訊號分析 37
3.2 模擬流程 39
3.2.1 模型平衡模擬 40
3.2.2 數據處理與分析 41
3.3 模擬結果與分析 42
3.3.1 拉壓無限長碳管數據處理與分析 42
3.3.2 施加特定模態予有限長碳管數據處理與分析 44
第四章 奈米線振動分析 62
4.1 模擬流程 62
4.2 分析方法 62
4.3 模擬結果與分析 63
第五章 結論與未來展望 78
5.1 初步結論 78
5.2 未來工作 79
參考文獻 80
附錄 84
A. 連續體振動理論 84
B. 其他尺寸邊界奈米碳管相關圖片 89

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